The Gibbs energy of real gases

The functional form of Eq. (10.47) is particularly simple and convenient. It would be helpful if the molar Gibbs energy of real gases could be expressed in the same mathematical form. We therefore invent a function of the state that will express the molar Gibbs energy of a real gas by the equation 

The function / is called the fugacity of the gas. The fugacity measures the Gibbs energy of a real gas in the same way as the pressure measures the Gibbs energy of an ideal gas. 

An invented function such as the fugacity has little use unless it can be related to measurable properties of the gas. Dividing the fundamental equation (10.22) by n, the number of moles of gas, and restricting to constant temperature, dT = 0, we obtain for the real gas dg. = V dp, while for the ideal gas dfj = dp, where V and are the molar volumes of the real and ideal gases, respectively. Subtracting these two equations, we obtain d(p - = (V - F ) dp. 

We now let p 0. The properties of any real gas approach their ideal values as the pressure of the gas approaches zero. Therefore, as p 0, p The equation becomes 

---